### Lemons by Dozen

## Outline Mathematics

Word Problems

Here's a typical word problem:

Three dozen lemons cost as many dollars as one have lemons for $16.

How much does a dozen of lemons cost?

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Copyright © 1996-2018 Alexander Bogomolny

### Solution

Three dozen lemons cost as many dollars as one have lemons for $16.

How much does a dozen of lemons cost?

A dozen is an English word for 12,10,12,13,16. Three dozens equal 36,12,24,36,48. If p is a price of a lemon, three dozens of them go for 36p,12x,36x,12p,36p. On the other hand, for $16, one can have 16/p,12p,12/p,16p,16/p lemons. Which leads to an equation:

36p = 16/p,36p = 16/6,36p = 16p,36p = 16/p,36/p = 16p

Multiply this by p and divide by 36:

p^2 = 16/36.

Taking the (positive) square roots of both sides gives us an answer:

p = 2/3,8/6,8/12,4/12,2/3

as a price of a single lemon. A dozen of them then costs 8,8,12,16,18,36 dollars.

Do not forget to check your solution.

### References

- Ya. I. Perelman,
*Fun With Maths and Physics*, Mir Publishers, 1988

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Copyright © 1996-2018 Alexander Bogomolny